Boolean Algebra Flashcards
What are the AND (∧) identities?
A ∧ 0 ⇒ 0
A ∧ 1 ⇒ A
What are the OR (∨) identities?
A ∨ 0 ⇒ A
A ∨ 1 ⇒ 1
What are the negation identities?
A ∧ ¬A ⇒ 0
A ∨ ¬A ⇒ 1
what is the absorption law?
A ∧ (A ∨ B) ⇒ A
A ∨ (A ∧ B) ⇒ A
What is the distribution law?
A ∧ (B ∨ C) ⇒ (A ∧ B) ∨ (A ∧ C)
(like multiplying out brackets)
what are De Morgan’s laws?
¬(A ∨ B) ⇒ ¬A ∧ ¬B
¬(A ∧ B) ⇒ ¬A ∨ ¬B
What is a half adder?
A circuit which adds two single bit binary numbers together
what are the input and outputs of a half adder?
Inputs:
- two single bit binary numbers (eg, A and B)
Outputs:
- S - the sum of the two numbers
- C - the carry bit
what is the logic diagram for a half adder composed of?
S = A XOR B
C = A AND B
How can you tell if a circuit is a half adder?
it has 2 inputs
what is a full adder?
a circuit used to add larger binary numbers together.
What are the inputs and outputs of a full adder?
Inputs:
- two single bit binary numbers (eg, A and B)
- the carry input bit (Cin)
Outputs:
- the Sum - S
- the carry output bit (Cout)
how can you tell a circuit is a full adder?
it has 3 inputs
what is a full adder made up of?
two half adders connected by an OR gate
what is a D-Type flip flop?
A circuit which stores one bit of data